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Search: id:A030182
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| A030182 |
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McKay-Thompson series of class 3B for Monster. |
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+0
3
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| 1, -12, 54, -76, -243, 1188, -1384, -2916, 11934, -11580, -21870, 79704, -71022, -123444, 421308, -352544, -581013, 1885572, -1510236, -2388204, 7469928, -5777672, -8852004, 26869968, -20218587, -30177684, 89408826
(list; graph; listen)
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OFFSET
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-1,2
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COMMENT
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Let t(q) = (eta(q)/eta(q^3))^12 = 1/q-12+54q-76q^2-243q^3+.... If j(q) is the j-invariant, with q-series given by A000521, then j(q) = (t+27)(t+243)^3/t^3 j(q^3) = (t+27)(t+3)^3/t. Hence t(q) can be used to parametrize the classical modular curve X0(3). - Gene Ward Smith (genewardsmith(AT)gmail.com), Aug 04 2006
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REFERENCES
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J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
N. D. Elkies, Elliptic and modular curves..., in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 38.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters. Comm. Algebra 18 (1990), no. 1, 253-278.
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FORMULA
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(eta(q)/eta(q^3))^12.
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CROSSREFS
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Essentially same as A007244, A045481.
Sequence in context: A066757 A045219 A054410 this_sequence A060171 A133078 A034436
Adjacent sequences: A030179 A030180 A030181 this_sequence A030183 A030184 A030185
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KEYWORD
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sign,nice,easy
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AUTHOR
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njas
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